Enhancing prediction of separation point location in thrust-optimized contoured nozzles with new realizability constants in the k-ω turbulence model

The objective of this study was to examine the capability of the realizable k–ω turbulence model to accurately predict the position of the separation point in hypersonic flows. While the two-equation k–ω model is suitable for predicting boundary flows with zero pressure gradients, its reliability decreases for flows with adverse pressure gradients, particularly in complex flows where normal stresses calculated using the Boussinesq approximation can become negative and “non-realizable” under high strain conditions. To address this problem, this study proposes a solution by introducing new variables in the Cμ formulation of the realizable model, which can limit eddy viscosity and enhance its sensitivity to the mean flow and turbulence models. We conducted numerical simulations and found that the realizable model produced improved results that were close to those of the experimental data. These findings highlight the potential of the new constants of the realizable k–ω turbulence model to accurately predict the location of compressible turbulent separation points in hypersonic flows.